Abstract
In this paper we describe Imogen, a theorem prover for intuitionistic propositional logic using the focused inverse method. We represent fine-grained control of the search behavior by polarizing the input formula. In manipulating the polarity of atoms and subformulas, we can often improve the search time by several orders of magnitude. We tested our method against seven other systems on the propositional fragment of the ILTP library. We found that our prover outperforms all other provers on a substantial subset of the library.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Andreoli, J.-M.: Logic programming with focusing proofs in linear logic. Journal of Logic and Computation 2(3), 297–347 (1992)
Andreoli, J.-M.: Focussing and proof construction. Annals of Pure and Applied Logic 107(1–3), 131–163 (2001)
Avellone, A., Fiorino, G., Moscato, U.: A new O(n log n)-space decision procedure for propositional intuitionistic logic. In: Kurt Goedel Society Collegium Logicum, vol. VIII, pp. 17–33 (2004)
Chaudhuri, K.: The Focused Inverse Method for Linear Logic. PhD thesis, Carnegie Mellon University, Technical report CMU-CS-06-162 (December 2006)
Chaudhuri, K., Pfenning, F.: Focusing the inverse method for linear logic. In: Ong, L. (ed.) Computer Science Logic, pp. 200–215. Springer, Heidelberg (2005)
Chaudhuri, K., Pfenning, F., Price, G.: A logical characterization of forward and backward chaining in the inverse method. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS, vol. 4130, pp. 97–111. Springer, Heidelberg (2006)
Degtyarev, A., Voronkov, A.: The inverse method. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, ch. 4, vol. I, pp. 179–272. Elsevier Science, Amsterdam (2001)
Dyckhoff, R.: Contraction-free sequent calculi for intuitionistic logic. Journal of Symbolic Logic 57(3), 795–807 (1992)
Garg, D., Murphy, T., Price, G., Reed, J., Zeilberger, N.: Team red: The Sandstorm theorem prover, http://www.cs.cmu.edu/~tom7/papers/
Harper, R., Honsell, F., Plotkin, G.: A framework for defining logics. Journal of the ACM 40(1), 143–184 (1993)
Howe, J.M.: Proof Search Issues in Some Non-Classical Logics. PhD thesis, University of St. Andrews, Scotland (1998)
Lamarche, F.: Games semantics for full propositional linear logic. In: Proceedings of the 10th Annual Symposium on Logic in Computer Science (LICS 1995), San Diego, California, pp. 464–473. IEEE Computer Society, Los Alamitos (1995)
Larchey-Wendling, D., Méry, D., Galmiche, D.: STRIP: Structural sharing for efficient proof-search. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS, vol. 2083, pp. 670–674. Springer, Heidelberg (2001)
Liang, C., Miller, D.: Focusing and polarization in intuitionistic logic. In: Duparc, J., Henzinger, T.A. (eds.) CSL 2007. LNCS, vol. 4646, pp. 451–465. Springer, Heidelberg (2007)
Maslov, S.Y.: An inverse method for establishing deducibility in classical predicate calculus. Doklady Akademii nauk SSSR 159, 17–20 (1964)
McCune, W.W.: OTTER 3.0 reference manual and guide. Technical Report ANL-94/6, Argonne National Laboratory/IL, USA (1994)
Pfenning, F., Schürmann, C.: System description: Twelf - A meta-logical framework for deductive systems. In: Ganzinger, H. (ed.) CADE 1999. LNCS, vol. 1632, pp. 202–206. Springer, Heidelberg (1999)
Raths, T., Otten, J.: The ILTP Library, http://www.iltp.de/
Raths, T., Otten, J., Kreitz, C.: The ILTP problem library for intuitionistic logic. J. Autom. Reasoning 38(1-3), 261–271 (2007)
Sahlin, D., Franzén, T., Haridi, S.: An intuitionistic predicate logic theorem prover. Journal of Logic and Computation 2(5), 619–656 (1992)
Tammet, T.: A resolution theorem prover for intuitionistic logic. In: McRobbie, M.A., Slaney, J.K. (eds.) CADE 1996. LNCS, vol. 1104, pp. 2–16. Springer, Heidelberg (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
McLaughlin, S., Pfenning, F. (2008). Imogen: Focusing the Polarized Inverse Method for Intuitionistic Propositional Logic. In: Cervesato, I., Veith, H., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2008. Lecture Notes in Computer Science(), vol 5330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89439-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-89439-1_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89438-4
Online ISBN: 978-3-540-89439-1
eBook Packages: Computer ScienceComputer Science (R0)